Problem: Simplify the following expression: $r = \dfrac{-45y^3 + 25y^2}{-15y^3}$ You can assume $y \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-45y^3 + 25y^2 = - (3\cdot3\cdot5 \cdot y \cdot y \cdot y) + (5\cdot5 \cdot y \cdot y)$ The denominator can be factored: $-15y^3 = - (3\cdot5 \cdot y \cdot y \cdot y)$ The greatest common factor of all the terms is $5y^2$ Factoring out $5y^2$ gives us: $r = \dfrac{(5y^2)(-9y + 5)}{(5y^2)(-3y)}$ Dividing both the numerator and denominator by $5y^2$ gives: $r = \dfrac{-9y + 5}{-3y}$